Design of a chatter-free terminal sliding mode controller for nonlinear fractional-order dynamical systems

Aghababa, Mohammad Pourmahmood

doi:10.1080/00207179.2013.796068

Cited by 85 publications

(50 citation statements)

References 44 publications

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“…Accordingly, following theorem provide sufficient conditions for robust synchronization between two fractional-order chaotic systems precisely at a prespecified time. (16) and (17) when D α = C 0 D α t will be obtained only if the controller in the slave system is chosen as:…”

Section: Controller Designmentioning

confidence: 99%

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A novel continuous time-varying sliding mode controller for robustly synchronizing non-identical fractional-order chaotic systems precisely at any arbitrary pre-specified time

Khanzadeh

Pourgholi

2016

Nonlinear Dyn

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In this paper, attempts are made to design a novel time-varying switching surface in sliding mode control which enables us to synchronize two fractional chaotic systems precisely at any arbitrary pre-specified time. For both Caputo (C) and Riemann-Liuville (RL) derivatives, control laws based on Lyapunov stability theorem are derived. The proposed method is completely robust against existence of uncertainties and exogenous disturbances due to eliminating the reaching phase. Since the sign function is replaced by fractional RL integral of the sign function, the chattering is removed. The simulation results in different scenarios are reported to show the effectiveness of the proposed method.

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Section: Controller Designmentioning

confidence: 99%

“…In [16][17][18] chattering free sliding mode control has been introduced. In [19][20][21] a reaching law for the reaching phase is established, and synchronization in [22] has complete robustness due to the elimination of the reaching phase.…”

mentioning

confidence: 99%

A novel continuous time-varying sliding mode controller for robustly synchronizing non-identical fractional-order chaotic systems precisely at any arbitrary pre-specified time

Khanzadeh

Pourgholi

2016

Nonlinear Dyn

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“…Based on the sliding mode control technique, a robust control scheme is designed for a class of fractional-order economical system with uncertainties and external disturbance in [10]. In [11], a finite-time control method is introduced for control of a class of non-autonomous fractional-order nonlinear systems in the presence of uncertainties and external noises. However, the uncertainties and external noises are assumed to be bounded in [10,11].…”

Section: Introductionmentioning

confidence: 99%

“…In [11], a finite-time control method is introduced for control of a class of non-autonomous fractional-order nonlinear systems in the presence of uncertainties and external noises. However, the uncertainties and external noises are assumed to be bounded in [10,11]. In addition, as discussed in [12], the finite-time synchronization is not possible.…”

Section: Introductionmentioning

confidence: 99%

Adaptive Fuzzy Control for Nonlinear Fractional-Order Uncertain Systems with Unknown Uncertainties and External Disturbance

Sun

2015

Entropy

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In this paper, the problem of robust control of nonlinear fractional-order systems in the presence of uncertainties and external disturbance is investigated. Fuzzy logic systems are used for estimating the unknown nonlinear functions. Based on the fractional Lyapunov direct method and some proposed Lemmas, an adaptive fuzzy controller is designed. The proposed method can guarantee all the signals in the closed-loop systems remain bounded and the tracking errors converge to an arbitrary small region of the origin. Lastly, an illustrative example is given to demonstrate the effectiveness of the proposed results.

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“…et al [43] discussed the fractional fuzzy adaptive SMC. Aghababa [44] designed a chatter-free terminal sliding mode controller for nonlinear fractional-order dynamical systems. The synchronization problems of FOHNNs have captured more and more researchers' attention [45][46][47][48].…”

Section: Introductionmentioning

confidence: 99%

Adaptive Synchronization for Uncertain Delayed Fractional-Order Hopfield Neural Networks via Fractional-Order Sliding Mode Control

Meng

Wang

2018

Mathematical Problems in Engineering

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Adaptive synchronization for a class of uncertain delayed fractional-order Hopfield neural networks (FOHNNs) with external disturbances is addressed in this paper. For the unknown parameters and external disturbances of the delayed FOHNNs, some adaptive estimations are designed. Firstly, a fractional-order switched sliding surface is proposed for the delayed FOHNNs. Then, according to the fractional-order extension of the Lyapunov stability criterion, a fractional-order sliding mode controller is constructed to guarantee that the synchronization error of the two uncertain delayed FOHNNs converges to an arbitrary small region of the origin. Finally, a numerical example of two-dimensional uncertain delayed FOHNNs is given to verify the effectiveness of the proposed method.

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Design of a chatter-free terminal sliding mode controller for nonlinear fractional-order dynamical systems

Cited by 85 publications

References 44 publications

A novel continuous time-varying sliding mode controller for robustly synchronizing non-identical fractional-order chaotic systems precisely at any arbitrary pre-specified time

A novel continuous time-varying sliding mode controller for robustly synchronizing non-identical fractional-order chaotic systems precisely at any arbitrary pre-specified time

Adaptive Fuzzy Control for Nonlinear Fractional-Order Uncertain Systems with Unknown Uncertainties and External Disturbance

Adaptive Synchronization for Uncertain Delayed Fractional-Order Hopfield Neural Networks via Fractional-Order Sliding Mode Control

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